WASHINGTON—Republicans and former Justice Department officials rallied around Attorney General Jeff Sessions as he continued to weather public criticism from President Donald Trump over his decision to recuse himself from investigations into Russia’s election interference, and other concerns.

The defenders voiced their support in response to a flurry of unusual attacks by a president on his top law-enforcement official, who was an early and ardent backer of Mr. Trump’s presidential campaign. In an interview Tuesday with The Wall Street Journal, Mr. Trump said he was “very disappointed in Jeff Sessions” for stepping aside from the probe into Russia’s meddling in the 2016 presidential election.

“I’m just looking at it,” the president said when asked how long he could continue to criticize Mr. Sessions without firing him. “I’ll just see. It’s a very important thing.”

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In an interview with The Wall Street Journal, President Trump continued to criticize Attorney General Jeff Sessions over his decision to recuse himself from any Russia related investigations. WSJ's Gerald F. Seib reviews what Mr. Trump said and explains how the situation may play out. Photo: T. J. Kirkpatrick for WSJ

Mr. Trump on Monday and Tuesday also tweeted that Mr. Sessions was “very weak” and “beleaguered” for not investigating his electoral opponent, Hillary Clinton, or those who leak intelligence information. During the campaign, Mr. Trump said Mrs. Clinton should be prosecuted and go to jail for sending classified information over a private email server she used as secretary of state. After winning the presidency, Mr. Trump reversed course and said he didn’t think his political rival should be investigated.

At his January confirmation hearing, Mr. Sessions said he would recuse himself on any pending investigation into Mrs. Clinton, saying that some of his comments during the campaign could lead to a perception of bias. Last summer, the Federal Bureau of Investigation concluded that Mrs. Clinton shouldn’t be prosecuted.

The Justice Department brought one leak case last month, when it charged a federal government contractor with providing classified information to a news organization.

Mr. Sessions couldn’t be reached for comment. Top aides said he has no plans to step aside and is focusing on running his department. In May as he became aware of the president’s displeasure, Mr. Sessions told Mr. Trump he would be willing to resign, according to people close to the attorney general. Mr. Trump declined the offer.

Mr. Trump’s nominee for another senior Justice Department post, Brian Benczkowski, at his confirmation hearing on Tuesday described Mr. Sessions as a “man of integrity who cares deeply about the institutional independence of the department.”

“I think he goes to work every day doing his dead-level best to protect that independence, and those sorts of comments are painful and difficult for me to hear,” Mr. Benczkowski said in response to questions about Mr. Trump’s tweets. At his hearing, Mr. Benczkowski faced questions about his work for a Russian bank.

At his news conference Tuesday afternoon, Mr. Trump said he was “disappointed” in Mr. Sessions and that “he should not have recused himself almost immediately after he took office.”

“If he was going to recuse himself, he should have told me prior to taking office, and I would have, quite simply, picked somebody else,” Mr. Trump said.

He added: “So I think that’s a bad thing, not for the president but for the presidency. I think it’s unfair to the presidency, and that’s the way I feel.”

The president’s sharp critiques raised questions about whether Mr. Sessions would resign or if Mr. Trump was laying the groundwork to fire him. Top elected Republicans said they hoped Mr. Trump would back off Mr. Sessions and chastised the president for urging the prosecution of Mrs. Clinton.

“The attorney general is doing a fine job and he made the right decision to recuse himself,” Senate Majority Leader Mitch McConnell (R., Ky.) said.

Lindsey Graham (R, S.C.), one of Mr. Trump’s most outspoken critics in the GOP, was among lawmakers who blasted the president’s treatment of Mr. Sessions. He also said it was “highly inappropriate” for Mr. Trump to tell the attorney general to go after his former Democratic opponent.

Sen. Orrin Hatch (R., Utah) said Mr. Sessions “is among the most honorable men in government today.”

“I have full confidence in Jeff’s ability to perform the duties of his office and, above all, uphold the rule of law,” Mr. Hatch said.

Former Justice officials said that Mr. Trump’s criticism has potentially eroded Mr. Sessions’ ability to lead the department. They were concerned that if Mr. Trump were to fire Mr. Sessions, other top Justice Department officials might resign in solidarity, creating a constitutional crisis.

They also said they were shocked that Mr. Trump would publicly attack a member of his own cabinet, especially one who supported his candidacy so early in the process and who has so aggressively promoted his platform of tougher policing and a crackdown on illegal immigration. Mr. Sessions as attorney general has hailed a new “Trump era” of stepped-up immigration enforcement, a central tenant of the business mogul’s campaign platform.

“What I am observing here is without precedent,” said Joe Whitley, a former top Justice Department official in Republican administrations.

John Yoo, a former top Justice Department official in the George W. Bush administration, said that Mr. Trump’s criticism “really undermines the attorney general’s position within his own department, and it also sends a terrible signal about the relationship between the White House and the Justice Department.”

If Mr. Sessions were fired or forced to resign, Mr. Trump would have a hard time finding a replacement that could be confirmed by the Senate, according to Mr. Yoo, a professor at the University of California Berkeley School of Law.

“The president would be in an enormous political hole,” Mr. Yoo said. “All of the other members of his cabinet would wonder who is next. And who is going to take a job to replace Sessions knowing this is how he treated the attorney general? And who can get confirmed?”

If Mr. Sessions were to step down or be fired, Deputy Attorney General Rod Rosenstein would become the acting attorney general. After Mr. Sessions recused himself from the Russia probe, it was supervised by Mr. Rosenstein. In May, shortly after Mr. Trump abruptly fired FBI Director James Comey, the deputy attorney general appointed Robert Mueller, a former FBI director, to become the special counsel overseeing the investigation.

Mr. Trump might be able to appoint another acting attorney general without Senate confirmation, if the Senate is closed for business for more than 10 days, but the chamber usually conducts pro forma sessions during recess to prevent any such appointments.

Mr. Trump could also move another Senate-confirmed official, from the Justice Department or any other department, to serve as acting attorney general for a limited time. But the pool of potential candidates is relatively small, and it is unclear who the White House might consider to make such an appointment.